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Question Number 155017 by SANOGO last updated on 24/Sep/21

$$\int_{\mathrm{0}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx};\:{avec}\:{E}\left({x}\right)\:{la}\:{partie}\:{entiere} \\$$

Answered by puissant last updated on 24/Sep/21

$${K}=\int_{\mathrm{0}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx} \\$$ $$=\int_{\mathrm{0}} ^{\mathrm{1}} {E}\left({x}^{\mathrm{2}} \right){dx}+\int_{\mathrm{1}} ^{\sqrt{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx}+\int_{\sqrt{\mathrm{2}}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx} \\$$ $$=\mathrm{0}\left(\mathrm{1}−\mathrm{0}\right)+\mathrm{1}\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)+\mathrm{2}\left(\frac{\mathrm{3}}{\mathrm{2}}−\sqrt{\mathrm{2}}\right) \\$$ $$=\mathrm{0}+\sqrt{\mathrm{2}}−\mathrm{1}+\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\:=\:\mathrm{2}−\sqrt{\mathrm{2}}.. \\$$ $$\:\:\:\:\therefore\because\:{K}\:=\int_{\mathrm{0}} ^{\frac{\mathrm{3}}{\mathrm{2}}} {E}\left({x}^{\mathrm{2}} \right){dx}\:=\:\mathrm{2}−\sqrt{\mathrm{2}}.. \\$$

Commented bySANOGO last updated on 24/Sep/21

$${merci}\:{bien}\:{courage} \\$$

Commented bypuissant last updated on 24/Sep/21

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Commented bytabata last updated on 25/Sep/21

$${sir}\:{how}\:{you}\:{give}\:{the}\:{interval}\:{in}\:{this}\:{form} \\$$ $${can}\:{you}\:{give}\:{me}\:{the}\:{formulla}\:{of}\:{E}\left({x}\right)\:? \\$$